It sounds like you're really close to a solution already...

... I execute a FlowTools command with system() function...

What is supposed to happen next is the application is to create an HTML file and email to the recipient...

... Once the submit button is pressed on the web page nothing more needs to be done, the forms job is over.

Instead of using system() to run the FlowTools command, write a simple wrapper script (separate from your CGI script), which will run FlowTools, build the HTML file of results and email that to the recipient. Then have your CGI script call that wrapper like this:

...
my $pid = fork;
if ( !defined $pid ) { 
    # maybe report an error to the browser...
}
elsif ( $pid == 0 ) {
    exec( 'wrapper_script', 'recipient@email', @other_args );
}
else {
    # print a simple HTML page to the client, saying that the job is
    # running and results will be emailed as soon as the job finishes
}
__END__
[download]

The point is that once the child starts, it'll handle everything that depends on the long-running process; meanwhile the parent CGI simply tells the client browser "okay, the job is running, you'll get email" and goes away.